2023/11/23 by Wataru Ichinose, Ichinose, Wataru
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Electrodynamics and Casimir Effect #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2311.13972
openalex publication_date 2023/11/23 · openalex created_date 2023/11/28 · openalex updated_date 2026/07/28
Feynman proposed a postulate or a method of quantization in his celebrated paper in 1948. Applying Feynman's postulate to temporally continuous quantum measurements of the positions of particles, Mensky proposed the restricted Feynman path integrals for continuous quantum measurements after phenomenological considerations. Our aim in the present paper is to give a rigorous proof that Mensky's restricted Feynman path integrals emerge out of the Feynman's postulate under a simple approximation. In addition, it is proved that the restricted Feynman path integrals emerge out of von Neumann's postulate on instantaneous measurements as well as Feynman's postulate. The quantum systems that we study include spin systems. These results are applied to formulations of the multi-split experiments, the quantum Zeno and the Aharanov-Bohm effects.